The Geometric and Hydrodynamic Shrinking Factors

In 1980, the g- and h-factors were defined in a slightly different102) manner making the direct application more feasible 

No restriction is made to the same molecular weight distribution. Instead of this, the natural distributions for f 2 and f = 2 are taken. For star-molecules, f = 2 corresponds to the monodisperse linear chain or to a linear chain that obeys the most probable distribution, and in the case of random polycondensates, f 2 corresponds to the branched non-fractionated sample, and f = 2 to the linear polycondensate. The g and h-factors so defined no longer have the appearance of shrinking factors in all cases, as may be recognized from Figs. 43 and 44. For star-molecules, both factors decrease as 

It may be emphasized here that the h-factor has become the more reliable parameter in spite of a less marked effect since with the recent photon-correlation spectroscopy, translational diffusion coefficients can be measured with a high accuracy and over the whole molecular weight range, from the monomer up to the largest molecular weights. 

The characterization of branched or cyclic structures by the g- and h-factors has the disadvantage that the properties of the analogous linear chains must be known. Such characterization requires a great deal of work in preparative chemistry as well as accurate physical chemical measurements, and in some cases the linear analogs are not even known. In such cases, a direct combination of the mean-square radius of gyration and the hydrodynamic radius leads to the very useful dimensionless parameter188.  

The effect of excluded volume on g for linear chains has been calculated, first more qualitatively by Weill and des Cloiseaux193 on the basis of scaling arguments, then by Akcasu and Benmouna202 quantitatively on the basis of the blob-model. The result is as follows 

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